A new algorithm for calibrating Gough platforms is proposed. It requires internal sensor measurements and only the position information provided by external sensors. It removes the need to measure orientation, which is intricate and error-prone, by algebraic elimination. This approach, relying on resultants and dialytic elimination, produces an equivalent, yet simpler, set of equations. Numerical simulation compares existing techniques using partial information to our method, which proves to be significantly more robust, without compromising accuracy: it reduces initial error in pose determination by $99\%$ and 80-98\%, in two sets of experiments with realistic conditions. We compare different choices for the measured configurations and show the relevance of configurations at the workspace's boundary. This increases reliability by avoiding to use any random measured configurations.